University of Tabriz Computational Methods for Differential Equations 2345-3982 Articles in Press 2025 05 07 Flexible fractional wavelet neural network for non-linear system identification 19780 10.22034/cmde.2025.64339.2915 EN Hasan Dadashzadeh Department of Mathematics, Payame Noor University, Tehran, Iran. Ghasem Ahmadi Department of Mathematics, Payame Noor University, Tehran, Iran. Yousef Edrisi Tabrizi Department of Mathematics, Payame Noor University, Tehran, Iran. Behrooz Rezaei Faculty of Electrical and Computer Engineering, Babol Noshirvani University of Technology, Babol, Iran. Journal Article 2024 11 04 This paper presents a novel neural network architecture called the flexible fractional wavelet neural network (FFrWNN), which enhances traditional wavelet networks by introducing two additional fractional wavelet parameters. These fractional parameters, along with the translation and scale parameters, are dynamically adjusted during the learning process, offering greater flexibility and improved approximation power. The network is trained using a stochastic gradient descent algorithm, and iterative online training formulas are developed for optimizing both the wavelet parameters and network weights. The stability of the network is proven through the Lyapunov stability approach, ensuring reliable convergence. The proposed FFrWNN is evaluated in the context of both one-dimensional and multi-dimensional dynamic system identification. Results demonstrate that the fractional wavelet parameters significantly improve the network's accuracy and efficiency. Compared to conventional neural networks, the FFrWNN shows superior performance in terms of precision and learning capability, making it a powerful tool for complex system modeling and signal processing applications. https://cmde.tabrizu.ac.ir/article_19780_c6575e9a6d77410c8c126c62f2578f26.pdf